The no-evolution models defined above have been very
useful as a baseline for comparing the predictions and observations made
by different workers, but, as the datasets available probe to higher
redshift,
evolutionary modeling has become increasingly important. These models take
as ingredients the stellar evolutionary tracks (normally for a restricted
metallicity range), the initial mass function, and a gas-consumption time
scale adjusted to give the present range of colors across the Hubble
sequence.
Assuming each galaxy evolves as an isolated system, the rest-frame SED can
be predicted at a given time, and thus an evolutionary correction can be
determined with respect to the no-evolution equations above, or the
predictions
can be incorporated in ab initio models to generate simulated data sets.
The cosmological model is a crucial, but often overlooked, variable in
linking time and redshift. For H0 = 70 and
= 0, the redshift
corresponding to a look-back time of, say, 7 Gyr, varies from z = 1-3
depending on .

A discussion of the reliability of these evolutionary
predictions and the differences between the various approaches is beyond
the scope of this review. Physical difficulties arise from the degenerate
effects of age and metallicity and the uncertainties of post-main sequence
stellar evolution. Results for various models have been intercompared by
Mazzei et al (1992),
Bruzual & Charlot
(1993),
and, most recently for populations of the same input age and
metallicity, by
Charlot et al (1996).
Recent efforts have concentrated on improving the stellar tracks and
spectral libraries
(Bruzual & Charlot
1993)
and including the effects of chemical evolution
(Arimoto et al 1992).
An all-inclusive database of progress in this area is presented by
Leitherer et al (1996).

For single burst populations presumed appropriate for early-type galaxies,
Charlot et al (1996)
discuss surprisingly large discrepancies in the predicted behavior of such
populations at times after 1 Gyr. The differences amount to at least 0.03
mag in rest-frame B-V, 0.13 mag in rest-frame V-K, and a 25% dispersion in
the V-band mass/light ratio. The large uncertainties in the predicted
optical-infrared
colors and visual luminosity evolution imply a significant age range (4-13
Gyr) that is permissible even for the simplest case of a passively evolving
red galaxy, emphasizing the continuing need to compare these models with
representative high redshift data, as well as the need to improve our
knowledge of post-main sequence stellar evolution.

For populations with constant star formation, both the
evolutionary corrections and the discrepancies between the available models
are less. This is because the same main sequence stellar types dominate the
spectra at most times and their theoretical behavior is considerably better
understood. Unfortunately, precise predictions are required for both types
of model galaxy (as well as the large range in between) because faint blue
galaxies could be either passively evolving systems seen at an early stage,
systems of constant star formation, or bursts of star formation imposed on
a quiescent system. A comparison of the predicted evolutionary behavior for
two of these cases is shown in Figure 3. Such
uncertainties represent a formidable obstacle to detailed modeling in
the ab initio approach.